Heat Capacity Measurement

What is heat capacity?

Definition: the heat capacity of a body is a quantity corresponding to the amount of energy in the form of heat that must be supplied or lost to obtain a temperature variation of one degree. It is also sometimes referred to as thermal capacity or specific heat.

This thermodynamic quantity depends on system’s conditions: temperature and pressure. It is often defined and measured at constant pressure (usually atmospheric). In this case, it is denoted Cp. More rarely, this property is defined at constant volume and denoted Cv.

The unit of thermal capacity is the quotient of energy (in Joules or calories) by a unit of temperature (in Kelvin or Celsius degree). Cp is also generally expressed in terms of mass (grams or kilograms), and is referred to as mass heat capacity. Its unit is often J/g/°C or J/g/K, but kJ/kg/°C is also sometimes used. Less often, it is expressed by volume or molar unit. It is then referred to as the volumetric or molar heat capacity.

Examples of mass heat capacities

Here are some examples of mass heat capacity values for common materials, gases, fluids and other substances:

How to measure thermal capacity?

The method or experiment used to measure a product’s heat capacity is calorimetry. A calorimeter enables precise measurement of the heat flow exchanged by the sample with the external environment during a controlled temperature change. Energy calibration is performed by measuring the Cp of materials whose value is precisely known as a function of temperature: water or sapphire.

Several experimental solutions are possible.

Thermal capacity measurement between isothermal steps

Isothermal step measurement involves using the calorimeter to perform isothermal steps, surrounding the desired measurement temperature. A heating or cooling ramp is performed between these steps. For example, to determine heat capacity at 20°C, a heating ramp is run between 2 isothermal steps at 18 and 22°C. By integrating the measured heat flux, the heat capacity at 20°C is calculated by dividing the integrated heat (in J) by the sample quantity/mass (in g) and the temperature delta covered (in °C or Kelvin).

The measurement requires a blank curve to subtract the thermal effect due to the asymmetry of the measured thermal signal linked to the system (calorimeter and measuring cells).

Ramp measurement

Ramp measurement consists in carrying out a heating or cooling ramp between 2 isothermal steps that are distant in temperature, and instead of integrating the measured heat flow, we use its value directly at each temperature. This has the advantage of permitting determination of heat capacity at all temperatures in the range covered by a single ramp. In reality, the range over which the ramp is made is not identical to that over which the thermal capacity can be calculated. The heating and cooling starting phases (at the start and end of the ramp) cannot be used. If possible, the temperature range explored should be extended in relation to the desired heat capacity measurement range.

This method is the one generally used in measurements carried out by Calnesis. This is also the one described in ASTM E1269.

Over what temperature range can Cp be measured?

At the Calnesis laboratory, heat capacity measurements are carried out by calorimetry at temperatures ranging from -80 to 600°C. To cover this wide range, several calorimeters, each with different characteristics, are used: DSC, microcalorimeter, Calvet calorimeter, etc. Beyond this range, other solutions are possible, such as using combined DSC-TGA apparatus. Don’t hesitate to ask us about it!

The calorimeter chosen for heat capacity measurement depends on the desired temperature range, but also on the characteristics of your samples: physical form, heterogeneity, etc.

Jean-Claude Neyt, COO and Lab Manager, Calnesis

What shape and size should the samples have for heat capacity measurement?

Calnesis adapts the choice of instrument and measuring cells to the temperatures of interest, and also to the shape of the samples: powders, pastes, liquids, solids, etc. The shape and size of crucibles and cells can vary between calorimeters (from a few µL to a few mL), and there are often different types for each calorimeter (stainless steel, hastelloy, alumina, etc.).

Thermal stability of samples

It is imperative that the samples analyzed are thermally stable over the entire temperature range explored. No phase change of system, such as solvent evaporation or thermal degradation, should occur during the temperature ramps. Indeed, the heat flux corresponding to these additional thermal effects would add to the heat flux due to the Cp, and distort the heat capacity calculation.

What is the expected accuracy of measurement?

Calnesis usually performs heat capacity measurements with an accuracy of less than 3%. This precision varies according to the type of calorimeter used, the temperature, but above all your samples (heterogeneity, physical state, etc.).

Bibliography

Experimental Data and Modeling of Solution Density and Heat Capacity in the Na–K–Ca–Mg–Cl–H2O System up to 353.15 K and 5 mol·kg–1 Ionic Strength
J. Chem. Eng. Data
DOI: 10.1021/acs.jced.7b00553